2018/04/24 by Mamakoukas, Giorgos, MacIver, Malcolm A., Murphey, Todd D.
#FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Robotics (cs.RO)
paper · doi:10.48550/arxiv.1804.09559
This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the second-order needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Lastly, the underactuated dynamic underwater vehicle model demonstrates convergence even in the presence of a velocity field.